so I've had to talk to this religous leader at a mosque about christianity because my parents want for me to convert back to islam, anyways he asked me this. You believe that no matter what a person does God will always forgive them? and what about the victim of their sin, what happens to them?
The answer to the question in your header, "No matter how badly a person sins, are they always forgiven?" as written, is "not necessarily". Jesus teaches in Mark 3:28-29 that all sins can be forgiven, except blasphemy of the Holy Spirit, but according to 1 John 1:5-9, Jesus blood cleanses us from all sin (v. 7b), but verse 9 makes it clear that confession is an essential and required antecedent of forgiveness. This is also demonstrated in Jesus teachings in Luke 18:10-14, where the tax collector made a confession of his sin, but the Pharisee did not, and Jesus praised the tax collector, and held the Pharisee in low regard. So, if you confess your sins, they will be forgiven.
As far as a person's victims, Christianity does not have as clear a statement on this. In Christianity, the teachings on the question of forgiveness of sin mostly relate to the sin against God, and not to the aspects of sins against our neighbors. But Jesus' teaching in Matthew (5:23-24) guides us that if we sin and harm our neighbor, that we should make matters right with him, before making our confession.